On Spectral Characterization of Nonuniform Hyperbolicity

Abstract

We give a complete functional theoretic characterization of tempered exponential dichotomies in terms of the invertibility of certain linear operators acting on a suitable Frech´et space. In sharp contrast to previous results, we consider noninvertible linear cocycles acting on infinite-dimensional spaces.The principal advantage of our results is that they avoid the use of Lyapunov norms.